So what do they wear?

One of the most common characteristics of those in clerical and religious vocations throughout history has been their custom of wearing clothing which differentiates them from the laity. In the late twentieth century, in the heart of the Progressive Era, there was a movement by some priest and religious to adopt the style of dress of the laity, which was generally a sign of heresy or at least a rebellion against orthodoxy. This short lived and generally abortive practice, almost none of the religious orders who adopted this convention survived past the middle of the twenty-first century, signaled the low point for religious vocations. In the decades and centuries that followed clerics and religious orders returned to the traditions of the past, with reasonable accommodations for their situation.
As it has been for centuries the Roman military collar, a "collarino" that covers a white collar almost completely, except for the top edge and a small white square at the base of the throat, is worn by priests of the Roman, Anglican Ordinate, and many other rites. The cossack, a traditional ankle length robe with a Roman collar, continues to be worn within Church environs as house dress. Outside, in the world, priest, at least diocesan priests, tend to wear clothing which matches local norms, with the exception that a Roman collar is worn. So if a shirt and slacks is the common business dress a priest will wear the same, though often in grey or black or some other color, with a Roman collar. In space it is not uncommon to see a priest in a black jumpsuit with a Roman collar.
Permanent deacons are not constrained to the wearing of religious attire except when actually engaged in their ministry. So while most possess a set or two of clerical garb most wear it only occasionally.
Religious clerics and brothers continue to wear the religious habit, most commonly consisting of a robe and cowl. In space the robe is often replaced by the more practical jumpsuit toped with a separate cowl which falls above the shoulders.
The garb of religious sisters tends to run to the traditional when in the convent or cloister and toward the veil and holy habit when in public. In space, where gravity fields may be variable, most women religious wear a two piece pajamas, typically in black or the color of their regular habit, often with a hair band instead of a veil. A crucifix or rosary is often part of the habit of many orders. A pin or badge is often affixed to the pajama top of many orders in place of this sacramental.